Georgakopoulos–Papasoglu's quasi-isometric bounded-treewidth conjecture

Let $G$ be a graph, and say that $G$ excludes a graph as an asymptotic minor if there is an integer $k$ such that the graph is not an asymptotic minor of $G$. Georgakopoulos–Papasoglu's conjecture. If there is an integer $k$ such that a graph $G$ excludes the $k\times k$ grid as an asymptotic minor, then $G$ is quasi-isometric to a graph of bounded treewidth. A counterexample to this conjecture has recently been constructed, so the asserted implication is false.